AbstractFor independent exponentially distributed random variables $X_i$ , $i𝟄 {\mathcal{N}}$ , with distinct rates ${λ}_i$ we consider sums $∑_{i𝟄\mathcal{A}} X_i$ for $\mathcal{A}⊆ {\mathcal{N}}$ which follow generalized exponential mixture distributions. We provide novel explicit results on the conditional distribution of the total sum $∑_{i𝟄 {\mathcal{N}}}X_i$ given that a subset sum $∑_{j𝟄 \mathcal{A}}X_j$ exceeds a certain threshold value $t>0$ , and vice versa. Moreover, we investigate the characteristic tail behavior of these conditional distributions for $t\to∞$ . Finally, we illustrate how our probabilistic results can be applied in practice by providing examples from both reliability theory and risk management.